In magnetic resonance imaging (MRI), the requirements for acquisition speed (or temporal resolution), spatial resolution and signal-to-noise ratio (SNR) often compete with each other. This competition is especially apparent in real-time MRI where spatial resolution and SNR performance may be sacrificed to achieve the temporal resolution needed to capture dynamic physiological events. For example, parallel imaging techniques such as SMASH [1] and SENSE [2] greatly reduce scan time, facilitating dynamic real-time imaging of rapid physiological processes such as cardiac motion. However, these techniques come with a SNR penalty and may compromise the diagnostic value of the images.
Filters based on linear transforms, such as the Fourier transform, are often used for image denoising. Spatial low-pass filters are commonly used to improve SNR of individual images [3]. In dynamic imaging, SNR may be further improved by temporal filtering. Averaging and spectral filtering are two commonly used Fourier transform based temporal filtering techniques [4].
Linear transform based filters have three common steps: (i) transform image/images to a linear combination of “modes”; (ii) truncate the insignificant “modes” and, (iii) inverse transform the remaining significant modes to reconstruct the filtered image/images. The optimal number of “modes” truncated in (ii) must balance the SNR improvement with image sharpness and fidelity. An optimal linear transform concentrates information into fewer “modes”, allowing more irrelevant “modes” to be truncated, and gives SNR gains with minimal information loss. The selection of the optimal transform and optimal filter cutoff are primary considerations in the design of any linear transform filters for image denoising.
Dynamic imaging of physiological processes generates series of images that usually show a high degree of temporal correlation. Physiological motion or signal changes are often periodic (e.g., cardiac or respiratory motion), or slowly varying (e.g., contrast agent-induced signal changes) compared to the temporal resolution of the imaging technique. Typically, either condition leads to series of images with substantially similar features in the temporal dimension.